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Quantum chemistry of the Fischer-Tropsch reaction catalysedby a stepped ruthenium surfaceCitation for published version (APA):Filot, I. A. W., Santen, van, R. A., & Hensen, E. J. M. (2014). Quantum chemistry of the Fischer-Tropsch reactioncatalysed by a stepped ruthenium surface. Catalysis Science & Technology, 4(9), 3129-3140.https://doi.org/10.1039/C4CY00483C

DOI:10.1039/C4CY00483C

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CatalysisScience &Technology

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PAPER View Article OnlineView Journal | View Issue

Catal. Sci. TechnoThis journal is © The Royal Society of Chemistry 2014

Laboratory of Inorganic Materials Chemistry, Schuit Institute of Catalysis,

Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven,

The Netherlands. E-mail: [email protected]

† Electronic supplementary information (ESI) available: Geometries and energiesof the initial, transition and final states used in the electronic structurecalculations. See DOI: 10.1039/c4cy00483c

Cite this: Catal. Sci. Technol., 2014,

4, 3129

Received 14th April 2014,Accepted 27th May 2014

DOI: 10.1039/c4cy00483c

www.rsc.org/catalysis

Quantum chemistry of the Fischer–Tropsch reactioncatalysed by a stepped ruthenium surface†

I. A. W. Filot, R. A. van Santen and E. J. M. Hensen*

A comprehensive density functional theory study of the Fischer–Tropsch mechanism on the corrugated

Ru(112̄1) surface has been carried out. Elementary reaction steps relevant to the carbide mechanism and

the CO insertion mechanism are considered. Activation barriers and reaction energies were determined for

CO dissociation, C hydrogenation, CHx + CHy and CHx + CO coupling, CHxCHy–O bond scission and

hydrogenation reactions, which lead to formation of methane and higher hydrocarbons. Water formation

that removes O from the surface was studied as well. The overall barrier for chain growth in the carbide

mechanism (preferred path CH + CH coupling) is lower than that for chain growth in the CO insertion

mechanism (preferred path C + CO coupling). Kinetic analysis predicts that the chain-growth probability

for the carbide mechanism is close to unity, whereas within the CO insertion mechanism methane will

be the main hydrocarbon product. The main chain propagating surface intermediate is CH via CH + CH

and CH + CR coupling (R = alkyl). A more detailed electronic analysis shows that CH + CH coupling is

more difficult than coupling reactions of the type CH + CR because of the σ-donating effect of the alkyl

substituent. These chain growth reaction steps are more facile on step-edge sites than on terrace sites.

The carbide mechanism explains the formation of long hydrocarbon chains for stepped Ru surfaces in the

Fischer–Tropsch reaction.

Introduction

The limited supply of readily available petroleum stimulatesthe search for alternative energy sources.1 Due to its abun-dance, natural gas is increasingly considered as a valuablealternative feedstock for the synthesis of fuels and chemicals.Synthesis gas (a mixture of CO and H2), which can be obtainedfrom natural gas by autothermal or steam reforming, can beused to produce long-chain hydrocarbons in the Fischer–Tropsch (FT) reaction.2–4 Several mechanistic proposals for thischain-growth reaction have been reviewed elsewhere.5 They canbe distinguished by the assumption of the inserting species inthe growing chain. The inserting species is either a CHx mono-mer derived from surface CO dissociation in the carbide mech-anism or an intermediate with the C–O bond intact in the COinsertion mechanism. The carbide mechanism involves disso-ciation of adsorbed CO, hydrogenation of the carbon adatomto a CHx building block and its insertion into the growinghydrocarbon chains on the surface. The chain reaction is

terminated by desorption of the hydrocarbon chain from thesurface as an alkene or alkane. An alternative termination path-way involves CO insertion, that results in aldehyde and alcoholproducts. In the CO insertion mechanism, chain propagationproceeds via insertion of a CO moiety and the C–O bond scis-sion therefore occurs after C–C coupling. This is in contrast tothe carbide mechanism, where C–O bond scission occurs priorto C–C coupling. Oxygen is predominantly removed from thesurface as water.5–8 The competing reaction is complete hydro-genation of the CHx surface intermediate to methane, which isan undesired by-product.

Good FT catalysts should exhibit high selectivity towardslong-chain hydrocarbons4,9 which requires facile CO dissocia-tion and slow chain-growth termination.10,11 Formation ofmethane, the undesired by-product of the FT reaction, shouldbe minimized. The self-organization of monomeric C1 speciesinto growing chains can be seen as a simple polymerizationprocess and the molecular weights of the hydrocarbon prod-ucts tend to follow the Anderson–Schulz–Flory (ASF) distribu-tion.12,13 Experimentally, it is usually found that the C1 and C2

product selectivities deviate from the ASF distribution.12,14–20

Two important schools of thought exist about the nature ofthe catalytically active surface. On the one hand, it is assumedthat the close-packed surfaces (terraces) are the activesites.21,22 Although metal atoms with low coordination num-bers are in principle more reactive, it has been argued that

l., 2014, 4, 3129–3140 | 3129

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http://dx.doi.org/10.1039/c4cy00483c

http://pubs.rsc.org/en/journals/journal/CY

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Fig. 1 Schematic representation of (left) the corrugated Ru(112̄1)surface and (right) the close-packed Ru(0001) terrace surface.

Catalysis Science & TechnologyPaper

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.View Article Online

these more reactive low-coordinated sites become blockeddue to their strong interaction with the adsorbed species and,in particular, with carbon adatoms. On the other hand, thehigh reactivity of low-coordinated sites, especially for CObond dissociation over stepped (B5) sites, is considered to becrucial to provide sufficient monomer building blocks tomaintain a high rate of chain growth.11,23–26

The mechanism of CO dissociation on metallic surfaceshas recently been elucidated. Experimental observations27,28

and theoretical calculations24,29,30 agree on the importance ofensembles of surface metal atoms arranged in such a waythat a stepped site is obtained for facile CO dissociation.These sites are usually called B5 sites. On such stepped sites ofCo and Ru surfaces, the direct dissociation of CO is favouredover the hydrogen-assisted alternative involving the formyl(CHO) intermediate.23,24,31,32 Although the discovery of theFischer–Tropsch reaction is almost a century ago, many openquestions remain about the reactions that lead to chain growthand chain-growth termination.

A large number of candidate reaction steps have been pro-posed for chain growth relevant to carbide and CO insertionmechanisms. Originally, Fischer and Tropsch proposed that sur-face CH2 couples with surface CH3.

2,33 Modern insights aboutsurface reactivity and theoretical chemistry advances now learnus that this proposal is incorrect, because the predicted barrierfor this coupling step is very high30 and, also, because the sur-face coverage of CH2 and CH3 is predicted to be low.34–36 Huand coworkers37 have explored various coupling reactions for arange of transition metal surfaces using Density Functional The-ory (DFT). Their analysis stresses the importance of the surfaceabundance of particular CHx species and, also, indicates thatstepped sites are preferred for C–C bond formation reactions forRu surfaces, with C + CH and CH + CH coupling being the mostfavourable pathways. On Co surfaces, however, CH2 + CH2 cou-pling and C + CH3 coupling are more likely candidates forchain growth. Saeys and co-workers have studied the CO inser-tion pathway on flat Co(0001) surfaces.38,39 CH2 + CO couplingwas found to be the most favourable pathway.38 The group ofMaitlis has performed extensive studies on the mechanisticaspects employing a model system using a Co homogeneouscatalyst.40–42 They found that the CH2 insertion into a surfacealkyl is the dominant mechanism. Water formation, which isrequired to remove O originating from CO dissociation, wasalso studied recently by DFT.43–46 It is generally proposed that,following OH formation, formation of adsorbed water occursmore favourably through proton migration between twohydroxyl adsorbates than via direct hydrogenation of thehydroxyl intermediate.

In the present theoretical study, we employed DFT toinvestigate all elementary reaction steps from syngas follow-ing the carbide as well as the CO insertion mechanism thatlead to formation of ethylene and ethane on a steppedRu(112̄1) surface. These reactions include the already well-studied CO dissociation and CH4 formation, because our aimis to build a database of kinetic parameters for all reactionsteps relevant to the FT reaction at the same computational

3130 | Catal. Sci. Technol., 2014, 4, 3129–3140

accuracy. We also study the hydrogenation of the surfaceintermediates towards olefinic and paraffin products andinclude formation of water, which removes O atoms from thesurface. We rationalize the experimentally observed lower C2

selectivity in the ASF distribution by considering how thereactivity of C3 surface intermediates will differ from that ofC2 intermediates. We explain the different kinetics of cou-pling reactions occurring on terraces and step-edge sites.Finally, we elaborate on the most likely FT pathway by com-paring the different FT reaction routes comprising both thecarbide and the CO insertion mechanism.

Method

Density Functional Theory (DFT) calculations were performedusing the Vienna Ab initio simulation package (VASP).47,48

The Perdew–Burke–Ernzerhof (PBE) exchange-correlation func-tional was employed for all calculations.49 To describe theinteraction between nuclei and core electrons, the projector-augmented wave (PAW) method was used.50,51 For the valenceelectrons a plane-wave basis set with an energy cut-off of400 eV and a Brillouin zone sampling of 5 × 5 × 1 k-points wereused. All elementary reactions were investigated on a steppedRu(112̄1) surface model (Fig. 1). The model for the stepped siteconsists of a slab with a thickness of at least 5 atomic layersand using a p(2 × 2) unit cell. To confirm that the thickness ofthe slab was sufficient, it was verified that the energy withrespect to the number of layers in the slab was converged. TheRu(112̄1) surface contains terrace and step-edge sites and isaccordingly representative for a dual reaction centre mecha-nism as explored earlier.10 In order to avoid spurious interac-tions between the images of the system, a vacuum layer of atleast 10 Å was added along the z-axis. To confirm that the vac-uum layer was large enough, it was verified that the electrondensity approached zero at the border of the unit cell. Toavoid dipole–dipole interactions between the super cells,adsorbates were placed on both sides of the surface retainingan inversion centre.

Ionic relaxation was carried out by the conjugate gradientmethod. During geometry optimization, all the degrees offreedom of the atoms in the slab as well as the adsorbed spe-cies were relaxed. To determine transition states, the nudged

This journal is © The Royal Society of Chemistry 2014




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elastic band (NEB) method as developed by Jónsson et al.was employed.52 The initial images between the optimizedinitial and final states were obtained via linear interpolation.The transition state was confirmed to be a saddle point onthe electronic energy surface by means of frequency analysis.Within VASP, this frequency analysis is performed byconstructing a Hessian matrix using the finite differenceapproach. We only considered the frequencies of theadsorbed species within this analysis as the contribution ofthe metal atoms can be neglected. Prior to investigating thelocation and properties of the transition states, the structureand energetics of a large number of adsorption models ofreactants, intermediates and products were determined.Based on these results, the initial guesses for the transitionstates were constructed.

Results and discussionDFT calculations

DFT calculations will be presented for the elementary reac-tion steps relevant to the carbide as well as the CO insertionmechanism of the Fischer–Tropsch reaction. The maingroups of reactions studied are (i) CO dissociation, (ii) Chydrogenation to CHx intermediate and CH4, (iii) CHx–CHx

coupling, (iv) CHx–CHx hydrogenation, (v) CHx–CO coupling,(vi) CHxCHyO hydrogenation, (vii) CHxCHy–O scission and(viii) O hydrogenation to H2O. For the carbide mechanism,reactions of groups (i), (ii), (iii), (iv) and (viii) are relevant.The CO insertion mechanism is covered by reaction of groups(i), (v), (vi), (vii) and (viii). We did not explore oxygen removalvia CO2 formation, because the CO2 selectivity for Ru cata-lysts in the FT reaction is low.13,53,54

CO dissociation

The energy barriers for CO dissociation are given in Table 1and correspond well with values reported before for thestepped Ru(112̄1) surface.23 Direct dissociation of CO is thepreferred route, because the hydrogen-assisted route involvesthe thermodynamically unfavourable formyl intermediate,resulting in a much higher overall barrier for CH formation.

C hydrogenation to CH4

Hydrogenation of adsorbed C to CH4 has been investigatedfor the Ru(112̄1) surface before.36 Here, we carried out thesecalculations at the same computational accuracy as for the


Table 1 Methanation pathway of synthesis gas on Ru(112̄1). The reported forfor the reactants and products

Index Elementary reaction

1 CO* + * → C* + O*2 C* + H* → CH* + *3 CH* + H* → CH2* + *4 CH2* + H* → CH3* + *5 CH3* + H* → CH4 + 2*

other elementary reaction steps. The forward and backwardactivation energies for the consecutive hydrogenation steps ofCHx (x = 0–3) to CHy (y = 1–4) are listed in Table 1.

The corresponding initial, transition and final states forthese reactions are given in the ESI† (Table S1). The activationenergies are with respect to the most stable adsorption site ofthe reacting surface adsorbates. In analogy with results forother transition metals, C hydrogenation to CH is relatively fac-ile. For Ru(112̄1), it is slightly endothermic. Further hydrogena-tion to CH2 (methylidene) is more difficult (Eact = 75 kJ mol−1)and endothermic by 38 kJ mol−1. This implies that at reason-able reaction temperatures surface CH2 and its hydrogenationproducts are much less abundant than C and CH surface inter-mediates. The barrier for the endothermic CH3 (methyl) forma-tion is 57 kJ mol−1. The barrier for CH4 formation, whichinvolves a single elementary reaction step recombining CH3

and H over a single Ru atom, has the highest barrier amongthe CHx hydrogenation steps (94 kJ mol−1).

CHx + CHy coupling reactions

A total of 10 reactions between CHx species were consideredfor carbon–carbon bond formation to describe chain growthin the carbide mechanism of the Fischer–Tropsch reaction(Table 2).

The corresponding initial, transition and final states aregiven in the ESI.† Reactions between CH2 and CH3 andbetween two CH3 (reactions 14 and 15) were not investigated,because it is well known that the interaction of the spatiallyextended C–H bonds in CH3 adsorbates results in repulsion,precluding C–C bond formation.55 Despite considerableefforts, we could not identify transition states for the follow-ing reactions: C + CH2, CH + CH2 and CH + CH3 coupling.We assume that these reaction will not occur on the Ru(112̄1)surface. It should be noted that these reactions have beenreported to be feasible on terrace surfaces.56 For theremaining five coupling steps C + C, C + CH, CH + CH, CH2 +CH2 and C + CH3 coupling, we identified six unique transi-tion states. For the CH + CH coupling step, two differentpathways were found (see Fig. 2).

The analogous coupling reaction involving longer chainsadsorbed on the surface are of the CH + CR type with R beingan alkyl group. Therefore, we investigated this latter reactionstep for R = CH3 in more detail in section 3.2. Table 2 showsthat the barrier for CH + CH coupling is substantially loweron the step-edge site than on the terrace surface. This

Catal. Sci. Technol., 2014, 4, 3129–3140 | 3131

ward and reverse energies are in relation to the most stable states found

Forward Eact (kJ mol−1) Backward Eact (kJ mol−1)

65 9040 3975 3757 4794 57




Table 2 CHx + CHy coupling reactions and their forward and backward activation energies for Ru(112̄1)

Index Elementary reaction Forward Eact (kJ mol−1) Backward Eact (kJ mol−1)

6 C* + C* → CC* + * 138 1447 C* + CH* → CCH* + * 129 758 C* + CH2* → CCH2* + * Not found9 C* + CH3* → CCH3* + * 92 11610a CH* + CH* → CHCH* + * (terrace) 149 11710b CH* + CH* → CHCH* + * (step) 86 5511 CH* + CH2* → CHCH2* + * Not found12 CH* + CH3* → CHCH3* + * Not found13 CH2* + CH2* → CH2CH2* + * 54 6014 CH2* + CH3* → CH2CH3* + * Not investigated15 CH3* + CH3* → CH3CH3* + * Not investigated

Fig. 2 Schematic representation of the two CH + CH couplingpathways on the Ru(112̄1) surface. The coupling of two CH moieties on(top) a terrace site and (bottom) a step-edge site. The black and whitespheres represent carbon and hydrogen atoms, respectively.

Fig. 3 Schematic representation of hydrogenation of adsorbedacetylene to ethane.


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preference for coupling on the step-edge site is in accordancewith several other works.37,57,58 Based on this insight, weinvestigated the other coupling reactions (reactions 6, 7, 9and 13) on the stepped surface as well. The most facile cou-pling reaction occurs between two methylidene species with abarrier of 54 kJ mol−1 (reaction 6). The barrier for the othercoupling reactions are higher: 86 kJ mol−1 for CH + CH, 92 kJmol−1 for C + CH3, 129 kJ mol−1 for C + CH and 138 kJ mol−1

for coupling of two carbon adatoms (C + C).

CHxCHy hydrogenation reactions

After formation of carbon–carbon bonds, higher hydrocarbonsmay leave the surface as olefins or paraffins (see Fig. 3). Weinvestigated such chain-growth termination steps for CHx–CHy

species. From CCH, a large number of hydrogenation routes toethylene and ethane needs to be considered. These possibilities


and the results of a reaction energy analysis are given inTable 3.

The structures of the involved stable and transition statesare collected in the ESI.† Hydrogenation of CCH to CCH2

(reaction 17) and CHCH to CHCH2 (reaction 19) have very simi-lar forward activation barriers around 82 kJ mol−1. While CCH2

formation is exothermic, CHCH2 formation is endothermic.Subsequent hydrogenation to CCH3 (reaction 18) and CHCH3

(reaction 20) proceeds with barriers of 19 and 62 kJ mol−1,respectively.

Comparatively, hydrogenation of CCH to CHCH and thereverse dehydrogenation of CHCH to CCH (reaction 21) arekinetically hindered with barriers of 140 and 162 kJ mol−1,respectively. Hydrogenation of CCH2 to CHCH2 (reaction 22)and of CCH3 to CHCH3 (reaction 23) have barriers of82 kJ mol−1. The reverse dehydrogenation reactions are veryfacile with barriers of 21 and 8 kJ mol−1, respectively. Thisimplies that CCHx intermediates are significantly more stablethan the corresponding CHCHx intermediates. This differ-ence draws similarity to the higher stability of adsorbed CHover CH2. Finally, we consider reactions that lead to forma-tion of ethylene (reaction 24) and ethane (reactions 25, 26and 27). Whereas ethylene formation proceeds with an activa-tion energy of 45 kJ mol−1 and is almost thermodynamicallyneutral, the hydrogenation of CHCH3 to CH2CH3 and, finally,CH3CH3 is endothermic. Although the first hydrogenationstep to CH2CH3 is facile and slightly exothermic, the second





Table 3 Hydrogenation reactions of C2 surface intermediates and their forward and backward activation energies for Ru(112̄1)


16 CC* + H* → CCH* + * 104 7217 CCH* + H* → CCH2* + * 82 12918 CCH2* + H* → CCH3* + * 19 419 CHCH* + H* → CHCH2* + * 83 4620 CHCH2* + H* → CHCH3* + * 62 3421 CCH* + H* → CHCH* + * 140 16222 CCH2* + H* → CHCH2* + * 82 2123 CCH3* + H* → CHCH3* + * 82 824 CHCH2* + H* → CH2CH2* + * 45 4225 CHCH3* + H* → CH2CH3* + * 19 2326 CH2CH2* + H* → CH2CH3* + * 58 3427 CH2CH3* + H* → CH3CH3* + * 112 71


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hydrogenation step toward ethane has to overcome a relativelyhigh barrier of 112 kJ mol−1. It is endothermic by 41 kJ mol−1.Alternatively, adsorbed ethylene can be further hydrogenatedto CH2CH3 (reaction 26). Although this reaction is facile withan activation barrier of 58 kJ mol−1, the reverse reaction ismore favourable with an activation energy of 34 kJ mol−1.

CHx + CO coupling

Three different reactions between CHx species and CO wereconsidered for chain propagation in the CO insertion mecha-nism (Table 4). These reactions all involve the migration ofadsorbed CO to a site adjacent to the CHx adsorption sitefollowed by C–C bond formation. Both carbon atoms in thefinal coupled CHx–CO species coordinate to surface Ruatoms. This strongly differs from mechanisms proposedbased on homogeneous mononuclear coordination com-plexes for CO insertion or migration.59

The corresponding initial, transition and final states are givenin the ESI.† The reaction between CH3 and CO (reaction 30)was not considered due to the expected steric repulsion. Themost facile CO insertion reaction is the C + CO coupling reac-tion (reaction 28) with a barrier of 138 kJ mol−1. The barrier forCH + CO coupling (reaction 29) and CH2 + CO coupling (reac-tion 30) are somewhat higher at 148 kJ mol−1 and 155 kJ mol−1,respectively. From comparison with the data in Table 2, it isimmediately clear that the barriers for CO insertion are signifi-cantly higher than those for CHx + CHy coupling (Table 2).Moreover, all CO insertion reactions are strongly endothermicby at least 77 kJ mol−1, implying that the rate constants for thereverse reactions are substantially higher.

CHx–CO hydrogenation

After CO insertion, the resulting CHxCO moiety can be hydro-genated to form a CHxCHyO species. We did not consider


Table 4 CHx + CO coupling reactions and their forward and backward activa

Index Elementary reaction

28 C* + CO* → CCO* + *29 CH* + CO* → CHCO* + *30 CH2* + CO* → CH2CO* + *31 CH3* + CO* → CH3CO* + *

formation of oxygenated products that can leave the surface,because their yield is usually very low under practical FT con-ditions. For each CHxCO* intermediate, the hydrogenation ofeither carbon atom was considered. This results in five differ-ent hydrogenation reactions (Table 5).

We could not identify a transition state for CCO* hydroge-nation (reaction 33). The orientation of the CCO* moiety inthe step-edge site (see the ESI†) prevents hydrogenation ofthe carbon atom of the CO group. The most difficult hydroge-nation step is that of CCO* to CHCO* (reaction 32), whichinvolves an activation energy of 104 kJ mol−1. The other reac-tions, i.e. the hydrogenation of CHCO* to CH2CO, that ofCHCO* to CHCHO* and finally the hydrogenation of CH2CO*to CH2CHO* proceed with lower activation energies of 95, 68and 63 kJ mol−1, respectively. All CHxCO hydrogenation reac-tions are endothermic.

CHxCHy–O bond scission

For chain growth to proceed, the C–O bond in the CHxCHyOsurface intermediate must first cleave. Five such elementaryreaction steps were considered for which results are listed inTable 6.

Among these reactions, it is most easy to cleave the C–Obond in CCO* with an activation energy of 52 kJ mol−1. TheC–O bond cleavage barriers for the other reactions are higher.All reactions are strongly exothermic, especially those for thepartially hydrogenated fragments.

Water formation

In the FT reaction, the surface oxygen atoms deriving fromCO dissociation are predominantly removed as water(Table 7). Water formation can proceed via two mechanisms,both involving intermediate OH formation from O and H(reaction 42) followed by either direct hydrogenation of OH


tion energy

Forward Eact (kJ mol−1) Backward Eact (kJ mol−1)

138 61148 44155 36Not investigated




Table 5 Hydrogenation reactions of CHxCO surface intermediates and their forward and backward activation energies for Ru(112̄1)


32 CCO* + H* → CHCO* + * 104 7733 CCO* + H* → CCHO* + * Not found34 CHCO* + H* → CH2CO* + * 95 4135 CHCO* + H* → CHCHO* + * 68 736 CH2CO* + H* → CH2CHO* + * 63 4

Table 6 CHxCHy–O bond scission and their forward and backward activation energies


37 CCO* + * → CC* + O* 52 12738 CHCO* + * → CCH* + O* 92 16339 CH2CO* + * → CCH2* + O* 77 24840 CHCHO* + * → CHCH* + O* 72 22541 CH2CHO* + * → CHCH2* + O* 65 234

Table 7 Elementary reaction steps leading to removal of water including their forward and backward activation energies


42 O* + H* → OH* + * 97 4943 OH* + H* → H2O* + * 89 1544 OH* + OH* → H2O* + O* + * 54 11


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to H2O (reaction 43) or via proton migration between two OHspecies to form H2O and O (reaction 44). The first hydrogena-tion step to produce adsorbed OH has a relatively high barrierof 97 kJ mol−1. The barrier for water formation via OH hydro-genation is 89 kJ mol−1. Comparatively, the reaction betweentwo hydroxyl groups is much more facile with a barrier of54 kJ mol−1. This suggests that water formation by reaction oftwo OH groups to H2O and adsorbed O is preferred.

Electron density difference analysis

To understand the differences in activation energies of the vari-ous elementary reaction steps, we investigated electron densitydifferences of selected reactions. Since the use of atomiccharges is not preferred as it is difficult to assign electrons to aspecific atom and chemical bonding typically involves contribu-tions of several molecular orbitals, it is more instructive to mapelectron density differences in space. We focus here on threeimportant issues relevant for the FT reaction. Firstly, we addressthe different reactivities of terrace and stepped sites. In particu-lar, we focus on the coupling step with the lowest activation bar-rier, i.e. CH + CH coupling. Secondly, we will compare CHcoupling with CH and CCH3 on stepped sites, because the latterreaction is relevant for formation of C3 products. Finally, we willhighlight the different adsorption strengths of ethylene andpropylene on stepped sites, which explains the lower thanexpected C2 selectivity observed during the FT reaction.

CH + CH coupling

The barriers for CH + CH coupling on stepped and terracesites of the Ru(112̄1) (Fig. 2) are 86 and 149 kJ mol−1,


respectively. Fig. 4a shows the electron density shifts thatresult from the formation of C–C bonds between two CH sur-face species in the corresponding transition state complexes.To determine these, the electron density distributions of thetwo separate CH fragments and the empty surface weresubtracted from the electron density distribution of the tran-sition state complex. It is seen that in the transition state forthe stepped site the electron density between the two C atomsis lowered and shifts to the metal atom. The correspondingshift in electron density for the transition state formation onthe terrace site is smaller. There are two reasons for this dif-ference. Firstly, it relates to the specific geometry of the transi-tion state complex on the stepped site, which results inincreased overlap between the bonding C–C orbitals and themetal d-band. Secondly, the coordinative unsaturation of thesurface metal atoms is higher for the stepped than for the ter-race surface. The decrease in electron density between the twoCH fragments by electron donation to the metal center resultsin decreased Pauli repulsion and, accordingly, in lower activa-tion energy for coupling.

CH + CH vs. CH + CCH3 coupling

We found that methylidyne (CH) coupling to the CCH3 sur-face intermediate (Fig. 4b) proceeds with lower barrier thanCH coupling to another CH species (65 vs. 86 kJ mol−1). InFig. 4a, the electron density shifts for C–C bond formation areshown. It can be seen that in the transition state for CH + CCH3

coupling more electron density is shifted from between the CHand CCH3 species to the metal atom relative to the CH–CH case.This difference is caused by the σ-donating effect of the methyl





Fig. 4 a. Electron density difference plots of the transition statefor CH + CH coupling on the terrace (left), step-edge (middle) and ofCH + CCH3 coupling on the step-edge (right) of the Ru(112̄1) surface.These plots were generated by subtracting the electron density of theindividual CH moieties on the surface from the electron density of thecomplex. Note that the electron density difference for the step-edgesite is larger than for the terrace site. 4b. Schematic representation ofCH–CH and CH–CCH3 coupling on a step-edge site of the Ru(112̄1)surface. The initial and final state of reaction are displayed.

Fig. 5 Electron density difference plots of the adsorbed states ofethylene (left) and propylene (right) on the Ru(112̄1) surface. Theseplots were generated by subtracting the electron density of theindividual complexes in vacuum and empty surface from the electrondensity of the complex. Note that the electron density difference forethylene is larger than for propylene.


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group. Consequently, the Pauli repulsion between CH andCCH3 is lower than between two CH fragments, explaining whythe barrier for coupling of the former two fragments is lower.

Ethylene vs. propylene desorption

Ethylene and propylene adsorb ‘side-on’ on a single Ru atomthrough interaction with their CC double bonds. Theadsorption energies of ethylene and propylene are 120 and100 kJ mol−1, respectively. The electron density shifts uponolefin adsorption are shown in Fig. 5. Here, the electron den-sity difference is determined by subtracting the electron den-sity of the adsorbate in the geometry it has in the adsorbedstate and the empty surface from the electron density of thesurface–adsorbate complex. The difference in electron densityfor ethylene is larger than for propylene. The reason for thedecreased electron density shift of the double bond inadsorbed propylene is the π-accepting nature of the CH3 sub-stituent. This results in weaker adsorption of propylene as


compared to ethylene. We expect that the stronger interac-tion of ethylene will result in increased surface residencetime of this fragment, which increases the probability of itschain growth relative to desorption and hydrogenation ascompared with that of its higher carbon number analogues.

Reaction energy diagrams

We constructed reaction energy diagrams based on the elemen-tary reaction steps explored in the DFT study (Tables 2–6).Fig. 6 shows the reaction energy diagram for formation of eth-ylene and water from CO and H2 in the carbide mechanism.For comparison, this diagram also contains the reaction path-way that leads to methane and water from synthesis gas. TheZPE (zero-point energy)-corrected overall reaction energies forethylene and methane formation are −212 and −217 kJ mol−1,respectively, which are close to thermodynamic data.

Fig. 7 shows that the preferred pathway for formation ofadsorbed CH2CH2 involves CH + CH coupling followed byhydrogenation to CH2CH2. The C + CH coupling reaction isvery unfavourable with a forward barrier of 129 kJ mol−1. Theoverall barrier for C + CH3 coupling is also unfavourable,because CH3 formation is endothermic and the barrier for itscoupling to C is also relatively high. Further reaction of CCH3

to CH2CH2 would involve the endothermic dehydrogenationto CCH2, followed by the endothermic hydrogenation toCHCH2 (Eact = 61 kJ mol−1) and the nearly thermoneutralhydrogenation step to adsorbed CH2CH2 with a barrier of45 kJ mol−1. Although coupling of two CH2 fragments is fac-ile, their formation is strongly endothermic. As C and CH arethe most stable surface intermediates yet coupling reactionsbetween C adsorbates are unfavourable, CH is predicted tobe the dominant chain propagation surface intermediate.The desorption energy of adsorbed ethylene is 120 kJ mol−1.The further hydrogenation of ethylene to ethane is includedin Fig. 6. The most difficult step towards ethane formation isthe hydrogenative desorption of CH2CH3 to CH3CH3 with anactivation energy of 112 kJ mol−1.





Fig. 6 Reaction energy diagram for ethane, ethylene and methane formation from carbon monoxide and hydrogen. A straight line indicates anadsorption/desorption reaction, whereas the parabolic lines denote a surface elementary reaction step. The adsorption/desorption energies as wellas the forward and backward activation energies are given. The detailed pathways for the reactions from adsorbed C* and CH* to CH2CH3* andCHCH2* are given in Fig. 7.

Fig. 7 Enlarged part of the reaction energy diagram showing variousroutes to ethane and ethylene formation. All data refer to the Ru(112̄1)surface.

Fig. 8 Reaction energy diagram for CHCH* formation from CO andH2. The various routes in the CO insertion mechanism are comparedto the CH–CH route in the carbide mechanism.


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Fig. 8 summarizes the pathways relevant to the CO inser-tion mechanism leading towards CHCH* formation in a reac-tion energy diagram. Similar to the carbide mechanism, thegrowing chain is initiated from adsorbed C*, which requiresCO dissociation. The most favourable path involves C + COcoupling followed by CC formation and its hydrogenation toCHCH. As CH together with C are the most stable CHx surface


intermediates, we also considered CH + CO coupling. The over-all barrier to CCH* formation via this route is higher becauseof the relatively low stability of the CHCO intermediate. Thispathway is nevertheless relevant to the CO insertion mecha-nism, because only the first coupling (i.e., C2 formation) can






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proceed via C + CO. Growth beyond C2 surface species will pro-ceed via CR + CO with R being an alkyl group, for which thebarrier of the CH + CO coupling is a reasonable estimate.Although the barrier for CH2 + CO coupling is only slightlyhigher than for the other considered coupling reactions, thelower surface stability of CH2 vs. C and CH results in a substan-tially higher overall barrier towards the product without theO atom, namely CH2C. The alternative pathway via CH2CHO iseven less favourable.

Comparison of these paths with that of chain growth viaCH + CH coupling (Fig. 8) clearly shows that the overall barrierfor CHCH formation via the carbide mechanism (63 kJ mol−1)is substantially lower than the preferred pathway via CO inser-tion (138 kJ mol−1). The CO insertion route is unfavourablebecause of the endothermicity of the CHx + CO coupling(Table 4) as well as of subsequent CHxCO hydrogenation reac-tions (Table 5).

Fig. 9 shows the reaction energy diagram for propyleneformation within the carbide mechanism. This diagraminvolves CH as the main inserting species in view of the lowbarrier for CH insertion into CCH3 species as compared tothe most favourable CH + CH pathway for C2 formation.Fig. 9 also shows that further growth of the CHCH2 surfaceintermediate is favoured over formation and desorption ofethylene. This already indicates that the computed kineticsare conducive to formation of long chain hydrocarbon prod-ucts on this surface. Compared to the C2 case, there will beless competition between chain growth of a C3 intermediate


Fig. 9 Reaction energy diagram for propylene from carbon monoxide and

and desorption of propylene, because the desorption energyof propylene is lower than that of ethylene. We expect thatthe adsorption energy of longer olefins will be very similar tothat of propylene. Qualitatively, the different balancesbetween chain growth and product desorption for C2 andhigher carbon number surface intermediates explains theexperimentally observed C2 selectivity below that of the ASFdistribution for the higher hydrocarbon products.12

Carbide vs. CO insertion mechanism

An important prerequisite for obtaining long hydrocarbonchains in the Fischer–Tropsch reaction is fast chain growthrate vs. chain-growth termination rate. This condition will leadto high values for the chain-growth probability α, defined as

i

i 1

(1)

where θi is the concentration of growing hydrocarbon chainswith length i.

We have earlier deduced explicit expressions for thechain-growth probability within the framework of lumped-sum kinetics for both the carbide and the CO insertion mech-anism.25,26,60 For the carbide mechanism, the expression is

Cp C

p C t

1

kk k

1

(2)


hydrogen. All data are for the Ru(112̄1) surface.




Fig. 10 Computed chain-growth probability (α) as a function of thesurface coverage of the chain propagating surface intermediate (CH inthe carbide mechanism and CO in the CO insertion mechanism). Theblack and red dotted lines indicate typical respective C1 and CO cover-age encountered under typical FT reaction conditions.


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where αC is the chain-growth probability in the carbidemechanism, kp the rate constant for CHx + CHy coupling,θC1

the surface concentration of C1 monomers and kt the ratefor chain-growth termination. For the CO insertion mecha-nism, we have deduced the expression

COp CO

p CO t

kk k

(3)

where αCO is the chain-growth probability in the CO inser-tion mechanism and θCO the surface concentration of CO.These formulas imply that a high α-value is obtainedwhen the rate constant for chain propagation (kp) is signif-icantly higher than the rate constant for chain-growth ter-mination (kt).

To determine the reaction rate constants for the chaingrowth steps in eqn (2) and (3), we determined the highestoverall barrier along the reaction pathway with respect to theenergy of the monomeric building block. These buildingblocks are surface CH and CO adsorbates, respectively, forthe carbide and CO insertion mechanisms (details on otherreaction steps and further assumptions are in the ESI†). Therate constants are listed in Table 8. Eqn (2) and (3) show thatthe chain-growth probability will also depend on the surfacecoverage of the chain propagating intermediate. To under-stand whether the proposed mechanisms can lead to desiredFischer–Tropsch products, we simply determined the chain-growth probability as a function of these surface coverages.The C1 coverage is reported to be below 10% under FTS con-ditions, whereas the CO surface coverage may be assumed tobe 90% or higher.11,26,60 Fig. 10 shows that the chain-growthprobability for the CO insertion mechanism is negligibleirrespective of the CO coverage. This analysis implies thatCHx hydrogenation to methane is strongly preferred overchain propagation with CO as the building block. On the con-trary, all three pathways with reasonable overall barrier forchain growth in the carbide mechanism, that is CH + CHcoupling (96 kJ mol−1), CH2 + CH2 coupling (126 kJ mol−1)and C + CH3 coupling (136 kJ mol−1) give greater than zerovalues for the chain-growth probability. At typical C1 coveragebelow 10%, the chain-growth probability is highest for theCH + CH coupling pathway.


Table 8 Rate constants computed at T = 220 °C for chain-propagationand chain-growth termination for the most favourable routes in carbideand CO insertion mechanisms

Route Mechanism kp [mol s−1] kt [mol s−1]

CHCH Carbide 6.79 × 102 5.88 × 10−4

CCH3 Carbide 4.51 × 10−1 5.88 × 10−4

CH2CH2 Carbide 3.94 × 10−2 5.88 × 10−4

CHCO CO insertion 1.74 × 10−8 5.88 × 10−4

CHCHO CO insertion 1.00 × 10−12 5.88 × 10−4

CH2CO CO insertion 3.80 × 10−13 5.88 × 10−4

CH2CHO CO insertion 5.84 × 10−17 5.88 × 10−4

Conclusions

DFT calculations were carried out for elementary reactionsteps of carbide and CO insertion mechanisms relevant tothe Fischer–Tropsch reaction on the stepped Ru(112̄1) sur-face. Activation barriers and reaction energies were deter-mined for CO dissociation, C hydrogenation, CHx + CHy andCHx + CO coupling, hydrogenation reactions of the surfaceintermediates, CHxCHy–O bond scission and O hydrogena-tion, which lead to formation of methane, higher hydrocar-bons including olefins and alkanes and water. The preferredpath for propagation in the carbide mechanism is CH + CHcoupling. Higher hydrocarbons are formed by CH insertioninto a CCH3 (or C(CH2)nCH3 equivalents) intermediate, whichis formed via a sequence of hydrogenation–dehydrogenationsteps of adsorbed CHCH. Coupling reactions of the type CH+ CCH3 are more favourable than CH + CH coupling, whichis attributed to the σ-donating effect of the alkyl substituent.CH + CH coupling is much more favourable n the steppedsite of the Ru(112̄1) surface than on the terrace site. The dif-ference originates from the stronger overlap of the formingπ-bonds between the CH fragments with the partially emptyd-orbitals of the more reactive metal surface atoms, resultingin decreased Pauli repulsion. The preferred coupling pathwayin the CO insertion mechanism involves the reaction betweenC and CO followed by facile C–O bond cleavage in CCO. Allthe CHxCO intermediates are relatively unstable on the sur-face as compared to CHx and CO, so that the overall barriersfor chain-growth via CO-insertion are much higher thanthose via CH + CH coupling. The kinetic consequence of thisdifference is that high chain-growth rate constants are pre-dicted for the carbide mechanism, whereas these are very lowfor the CO insertion mechanism. This kinetic analysis pre-dicts methane to be the main product during CO hydrogena-tion within the CO insertion mechanism. With kineticparameters computed for the carbide mechanism, highchain-growth probability is predicted. The carbide mechanism






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explains the formation of long hydrocarbon chains on thestepped Ru surface.

Acknowledgements

NWO is acknowledged for providing access to the supercom-puter facilities.

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